Anon, Fourier and Laplace Transforms, Solution Manual (free). Anon, Fourier Series. Anon, The Fourier Transform and its Applications (free). Anon, The Fourier.
Problems and Solutions This page records my personal solutions to the textbook problems. As a mathematician, I strongly recommend any reader should 'DO' these exercises 'In Your Way' before read other guys' answers!!
After solving the exercises, I also discuss on the connection between exercises and other known theorems or perspectives, for example, Exercise 5.16 in Evans' PDEs or Chapter 6 of Folland's Real Analysis. I believe this will bring more fun and communications between us. Corrections, Comments and improvements are welcome!!! Partial Differential Equations. Chapter 3.
Chapter 4. Chapter 5 (Completed!). Chapter 6 (Completed!). Chapter 7 (97% Completed!). Chapter 8.
Chapter 9. Chapter 10. Chapter 11 Systems of Conservation Laws.
Chapter 12 Last Modified: 2018. 05.
Chapter 2 (Incomplete). Chapter 3 (Incomplete). Chapter 4 (Incomplete). Chapter 6 (Incomplete). Chapter 7 (Incomplete). Chapter 8 (Incomplete) Last Modified: 2017. Chapter 2.
Chapter 3. Chapter 4 Holder Estimates.
Chapter 5 Existence, Uniqueness and Regularity of Solutions. Chapter 6 Further Theory of Weak Solutions.
Chapter 7 Strong Solutions. Chapter 8 Fixed Point Theorems and Their Applications Last Modified: 2016. 10. Chapter 2.
Chapter 3 Symmetry for a Non-Linear Poisson Equation in a Symmetric Set. Chapter 4 Symmetry for the Non-Linear Poisson Equation in R^n. Chapter 5 Monotonicity of Positive Solutions in a Bounded Set. Appendix A On the Newtonian Potential. Appendix B Rudimentary Facts about Harmonic Fucntions and the Poisson Equation. Appendix D On the Divergence Theorem and Related Matters Last Modified: 2017.
Stochastic Analysis And Applications
22 Dispersive Equations. Chapter 1 (Incomplete). Chapter 2 (Incomplete). Chapter 3 (Incomplete). Chapter 4 (Incomplete). Chapter 5 (Incomplete).
Chapter 6 (Incomplete). Chapter 7 Korteweg-de Vries Equation. Chapter 8 Asymptotic Behavior of Solutions for the k-gKdV Equations. Chapter 9 Other Nonlinear Dispersive Models. Chapter 10 General Quasilinear Schrodinger Equation Last Modified: 2017.
Fourier Analysis Pdf
Undergraduate and graduate students interested in studying the Fourier transform. This book presents the theory and applications of Fourier series and integrals, eigenfunction expansions, and related topics, on a level suitable for advanced undergraduates. It includes material on Bessel functions, orthogonal polynomials, and Laplace transforms, and it concludes with chapters on generalized functions and Green's functions for ordinary and partial differential equations. The book deals almost exclusively with aspects of these subjects that are useful in physics and engineering, and includes a wide variety of applications. On the theoretical side, it uses ideas from modern analysis to develop the concepts and reasoning behind the techniques without getting bogged down in the technicalities of rigorous proofs.Hardcover: 433 pages Publisher: American Mathematical Society (January 13, 2009).